Jose Manuel Gordillo

A new device for the generation of microbubbles

In this paper we present a new method for the production of bubble-liquid suspensions (from now on BLS) composed of micron-sized bubbles and with gas to liquid volume ratios larger than unity. We show that the BLS gas fraction λ=Qg/Ql, being Qg and Ql the flow rates of gas and liquid, respectively, is controlled by a dimensionless parameter which accounts for the ratio of the gas pressure inside the device to the liquid viscous pressure drop from the orifices where the liquid is injected to the exit, where the BLS is obtained. This parameter permits the correct scaling of the BLS gas volume fraction of all the experiments presented.

Axisymmetric Bubble Pinch-Off at High Reynolds Numbers

Analytical considerations and potential-flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, rn, decreases as tau proportional to r2n sqrt[1lnr2n], where tau is the time to break up, when the local shape of the bubble near the singularity is symmetric. However, if the gas convective terms in the momentum equation become of the order of those of the liquid, the bubble shape is no longer symmetric and the evolution of the neck changes to a rn proportional to tau1/3 power law. These findings are verified experimentally.

Scaling the drop size in coflow experiments

We perform extensive experiments with coflowing liquids in microfluidic devices and provide a closed expression for the drop size as a function of measurable parameters in the jetting regime that accounts for the experimental observations; this expression works irrespective of how the jets are produced, providing a powerful design tool for this type of experiments.

High-speed jet formation after solid object impact.

A circular disc hitting a water surface creates an impact crater which after collapse leads to a vigorous jet. Upon impact an axisymmetric air cavity forms and eventually pinches off in a single point halfway down the cavity. Two fast sharp-pointed jets are observed shooting up- and downwards from the closure location, which by then has turned into a stagnation point surrounded by a locally hyperbolic flow pattern. This flow, however, is not the mechanism feeding the jets. Using high-speed imaging and numerical simulations we show that jetting is fed by the local flow around the base of the jet, which is forced by the colliding cavity walls. We show how the well-known theory of a collapsing void (using a line of sinks on the symmetry axis) can be continued beyond pinch-off to obtain a new and quantitative model for jet formation which agrees well with numerical and experimental data.

Generation and breakup of Worthington jets after cavity collapse. Part 1. Jet formation

At the beginning of the last century Worthington and Cole discovered that the high-speed jets ejected after the impact of an axisymmetric solid on a liquid surface are intimately related to the formation and collapse of an air cavity created in the wake of the impactor. In this paper, we combine detailed boundary-integral simulations with analytical modelling to describe the formation of such Worthington jets after the impact of a circular disk on water. We extend our earlier model in Gekle et al. (Phys. Rev. Lett., vol. 102, 2009a, 034502), valid for describing only the jet base dynamics, to describe the whole jet. We find that the flow structure inside the jet may be divided into three different regions: the axial acceleration region, where the radial momentum of the incoming liquid is converted to axial momentum; the ballistic region, where fluid particles experience no further acceleration and move constantly with the velocity obtained at the end of the acceleration region; and the jet tip region, where the jet eventually breaks into droplets. From our modelling of the ballistic region we conclude that, contrary to the case of other physical situations where high-speed jets are also ejected, the types of Worthington jets studied here cannot be described using the theory of hyperbolic jets of Longuet-Higgins (J. Fluid Mech., vol. 127, 1983, p. 103). Most importantly, we find that the velocity and the shape of the ejected jets can be well predicted at any instant in time with the only knowledge of quantities obtained before pinch-off occurs. This fact allows us to provide closed expressions for the jet velocity and the sizes of the ejected droplets as a function of the velocity and the size of the impactor. We show that our results are also applicable to Worthington jets emerging after the collapse of a bubble growing from an underwater nozzle, although this system creates thicker jets than the disk impact.

Linear stability of co-flowing liquid-gas jets

A temporal, inviscid, linear stability analysis of a liquid jet and the co-flowing gas stream surrounding the jet has been performed. The basic liquid and gas velocity profiles have been computed self-consistently by solving numerically the appropriate set of coupled Navier–Stokes equations reduced using the slenderness approximation. The analysis in the case of a uniform liquid velocity profile recovers the classical Rayleigh and Weber non-viscous results as limiting cases for well-developed and very thin gas boundary layers respectively, but the consideration of realistic liquid velocity profiles brings to light new families of modes which are essential to explain atomization experiments at large enough Weber numbers, and which do not appear in the classical stability analyses of non-viscous parallel streams. In fact, in atomization experiments with Weber numbers around 20, we observe a change in the breakup pattern from axisymmetric to helicoidal modes which are predicted and explained by our theory as having an hydrodynamic origin related to the structure of the liquid-jet basic velocity profile. This work has been motivated by the recent discovery by Ganan-Calvo (1998) of a new atomization technique based on the acceleration to large velocities of coaxial liquid and gas jets by means of a favourable pressure gradient and which are of emerging interest in microfluidic applications (high-quality atomization, micro-fibre production, biomedical applications, etc.).

Aerodynamic effects in the break-up of liquid jets: on the first wind-induced break-up regime

We present both numerical and analytical results from a spatial stability analysis of the coupled gas–liquid hydrodynamic equations governing the first wind-induced (FWI) liquid-jet break-up regime. Our study shows that an accurate evaluation of the growth rate of instabilities developing in a liquid jet discharging into a still gaseous atmosphere requires gas viscosity to be included in the stability equations even for low

Transition from bubbling to jetting in a coaxial air–water jet

{\it We}_g

Monodisperse microbubbling: Absolute instabilities in coflowing gas–liquid jets

, where

Axisymmetric bubble collapse in a quiescent liquid pool. II. Experimental study

{\it We}_g{=}\rho_gU_l^2R_0/\sigma